Unusual mechanical stability of a minimalRNA kissing complexPan T. X. Li*, Carlos Bustamante*†§, and Ignacio Tinoco, Jr.*¶

Departments of *Chemistry and †Physics and Molecular and Cell Biology, and §Howard Hughes Medical Institute,University of California, Berkeley, CA 94720

Contributed by Ignacio Tinoco, Jr., August 28, 2006

By using optical tweezers, we have investigated the mechanicalunfolding of a minimal kissing complex with only two G�C basepairs. The loop–loop interaction is exceptionally stable; it is dis-rupted at forces ranging from 7 to 30 pN, as compared with 14–20pN for unfolding hairpins of 7 and 11 bp. By monitoring unfolding�folding trajectories of single molecules, we resolved the interme-diates, measured their rate constants, and pinpointed the rate-limiting steps. The two hairpins unfold only after breaking theintramolecular kissing interaction, and the kissing interactionforms only after the folding of the hairpins. At forces that favor theunfolding of the hairpins, the entire RNA structure is kineticallystabilized by the kissing interaction, and extra work is required tounfold the metastable hairpins. The strong mechanical stability ofeven a minimal kissing complex indicates the importance of suchloop–loop interactions in initiating and stabilizing RNA dimers inretroviruses.

mechanical unfolding � optical tweezers � RNA dimerization �single molecule � RNA folding

Tertiary interactions enable RNA to form long-range contactsand thereby form complex structures. However, thermody-

namic and kinetic information for these interactions is scarce (1).Recent developments in single-molecule techniques allow a closelook at the folding of individual RNA molecules (2–4). Particularly,the application of force to single-ribozyme molecules by opticaltweezers (3) revealed the detailed unfolding pathways of this 390-ntRNA in nondenaturing solutions at physiological temperatures. Itremains a challenge, however, to study the kinetics of individualsteps in folding an RNA with complicated tertiary structures.

A kissing interaction, a basic type of RNA tertiary contact, is thebase-pairing formed by complementary sequences in the apicalloops of two hairpins (5). Intramolecular kissing complexes havebeen found in many RNA structures, ranging from 75-nt tRNAs (6,7) to megadalton ribosomes (8); intermolecular kissing interactionsalso are critical for many biological processes (reviewed in ref. 5),such as dimerization of retroviral genomic RNAs (9, 10). Thesimplest kissing interaction is formed between a pair of hairpinseach with a GACG tetraloop (11). The third and fourth nucleotidesin the loop form two G�C base pairs with their counterparts fromthe other hairpin. This minimal kissing interaction was initiallyfound in the genomic RNA of Moloney murine leukemia virus(MMLV), an extensively studied retrovirus (12) and one of the mostused vectors for gene therapy (13). The 5� UTR of the MMLVgenomic RNA contains four closely spaced stem loops (SL-A–SL-D) (14), each of which is capable of forming a kissing interactionwith its counterpart in another copy of the genomic RNA (11, 15,16). This region, including the two hairpins with GACG loops(SL-C and SL-D), serves both as the RNA dimerization initiationsite (DIS) and as the RNA encapsidation signal (�) (17, 18).

The kissing hairpins are evolutionarily conserved in the DISregion of retroviruses, and mutational disruption of the kissingusually compromises the viral packaging, viability, and infectivity(9). However, because these homodimeric kissing complexes arestructurally rearranged into more stable extended duplexes in themature viral particle (9, 10), they are frequently labeled as labile or

metastable dimer intermediates. So how stable are the kissingcomplexes? To address this question, we used an optical tweezerstechnique to test the mechanical stability of a minimal kissingcomplex.

Based on the kissing complexes formed by SL-C and SL-Dhairpins (11, 16), we designed an RNA (KC30) containing twohairpins linked by 30 A-rich nucleotides (Fig. 1). The two hairpins,each with a GACG loop, can form an intramolecular kissingcomplex. The linker between the hairpins allowed refolding of thekissing complex after the RNA unkissed such that a kissing complexcan be repeatedly unfolded and refolded many times. To avoidadding strain to the kissing structure, the linker was designed toavoid secondary structure; it was roughly twice as long as theend-to-end distance of the kissing hairpins. We assume that thehelical axes of the two hairpins are parallel to the direction ofapplied force, in contrast to the unzipping of a hairpin, during whichthe axis of the hairpin is perpendicular to the force (1). The KC30RNA, flanked by two �500-bp DNA�RNA handles, was tetheredto two micrometer-sized polystyrene beads through affinity inter-actions (2) (Fig. 1). The two beads were held by a dual-beam opticaltrap and a micropipette, respectively (2, 19). Movement of themicropipette changed the extension of the molecule and generatedtension. The folding reaction was studied at 22°C in a flow chambercontaining a buffer of 10 mM Hepes (pH 8.0) and 250 mM KCl, in

Author contributions: P.T.X.L., C.B., and I.T. designed research; P.T.X.L. performed research;P.T.X.L. and I.T. analyzed data; and P.T.X.L. and I.T. wrote the paper.

The authors declare no conflict of interest.

Abbreviations: MMLV, Moloney murine leukemia virus; DIS, dimerization initiation site;SL, stem loop.

¶To whom correspondence should be addressed. E-mail: intinoco@lbl.gov.

© 2006 by The National Academy of Sciences of the USA

Fig. 1. Experimental setup. KC30 RNA contains two hairpins linked by 30A-rich nucleotides. The GACG loops of the two hairpins can form a kissingcomplex. This RNA is flanked by double-stranded DNA�RNA handles, throughwhich the entire molecule can be tethered between two microspheres byaffinitive interactions. The streptavidin-coated bead was held by a force-measuring trap (28). The digoxigenin-coated bead was mounted on a micropi-pette. By moving the piezoelectric flexure stage on which the micropipettewas attached, force was exerted on the RNA in the direction shown by thearrows. The drawing is not to scale.

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which the structure of the minimal kissing complex formed by a pairof unlinked hairpins was determined (3).

Force–Extension PatternsIn force-ramp experiments, an RNA molecule was repeatedlystretched and relaxed. When the double-stranded handles alonewere pulled, the force increased monotonically with extension (2),as typically described by a worm-like-chain interpolation formula(20). Unfolding an RNA structure suddenly increased the extensionof the molecule, resulting in a ‘‘rip’’ on the force–extension curve.Similarly, a ‘‘zip’’ that decreased the extension indicated a foldingstep. Such changes in the extensions caused the trapped bead toquickly move either toward or away from the center of the trap, thusaltering the force. Therefore, in the force–extension curves, bothrip and zip transitions have negative slopes, in sharp contrast to theelastic stretching of the handles. After the RNA was unfolded intoa single strand, the force again increased monotonically with theextension to �60 pN (2, 3, 21).

Several transitions were observed in the force–extension curvesof KC30 RNA (Fig. 2 a–c). To relate these transitions to thestructural changes, we pulled individual hairpins and a pair ofhairpins that cannot form kissing interactions (Fig. 2 d–f). Hairpin1, containing 11 base pairs and a tetraloop, unfolds and refoldsseveral times between 16 and 20 pN with a change in extension, �X,of �9–10 nm. The value of �X is consistent with the value estimatedfrom a worm-like-chain model (20) using a persistence length of 1nm and a contour length of 0.59 nm per nucleotide (2). The manyunfolding�refolding transitions within a few piconewtons indicatesthe bistability of the hairpin: Free energies of unfolded and folded

states at these forces are very close, and the kinetic barrier betweenthe two states is low. Such quick transitions between the two stateswas previously termed ‘‘hopping’’ (2). The transition force ofhairpin 2 ranges from 14 to 18 pN. �X for unfolding this hairpin withseven base pairs is �4–5 nm. The equilibrium force, F1/2, at whichunfolding and refolding rates are equal, is 17.6 � 0.1 pN for hairpin1 and 16.0 � 0.1 pN for hairpin 2. In the two-hairpin KC30AARNA, the apical loop of hairpin 2 was mutated from GCAG toGAAA. As expected, formation of the two hairpins but not thekissing interaction was observed in the folding of this RNA.

The experiments on the individual hairpins and the mutantlacking the complementary loops make the transitions on theforce–extension curves of KC30 RNA interpretable (Fig. 2 a–c).When force was relaxed from 30 pN (green curves), the twohairpins formed first between 20 and 14 pN. The third transitionwith �X of �7 nm, which occurred at 5–10 pN, represents thekissing interaction between the two hairpins. On extension, threetypes of force–extension curves were observed. The first type ofcurve displays three transitions: a rip of �10 nm at �7–17 pNfollowed by unfolding of the two hairpins. This first rip indicates theunkiss, i.e., the disruption of the kissing interaction. The secondtype of unfolding curve shows only two transitions: In the first one,the kiss and hairpin 2 appear to be unfolded in a single step (15–20nm, double transition); �X of the second transition is similar to theunfolding of hairpin 1. Only a single, big rip appears in the third typeof unfolding trajectory. The �X of this rip (�30 nm) is consistentwith the entire RNA being unfolded in a single step (tripletransition). To confirm the unkiss and kissing transitions, werepeated the pulling experiments but only relaxed the force to �10pN to prevent the kissing. As expected, such trajectories show onlythe folding and unfolding of the two hairpins, similar to theKC30AA mutant (data not shown). This observation clearly indi-cates that the kissing interaction only occurs after the formation ofthe hairpins (Fig. 3a).

In contrast, in all three types of mechanical unfolding curves ofKC30 RNA, the first transition always includes the unkiss, suggest-ing that the hairpins cannot be unfolded before the kissing inter-action is disrupted. The unfolding trajectories can be explained by

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Fig. 2. Force–extension curves of KC30 RNA and its mutants. (a–c) The typicaltrajectories of KC30 RNA. Three types of unfolding (blue) curves were ob-served, but all refolding (green) follow the same pathway. (d–f ) The unfold-ing�refolding curves of hairpin 1, hairpin 2, and KC30AA RNA. KC30AA RNAis identical to KC30, except the apical loop of hairpin 2 is mutated to GAAA toprevent the formation of the kissing interaction.

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Fig. 3. Three types of unfolding trajectories of KC30 RNA. (a) Unfolding andrefolding pathways. The first apparent transition can contain one, two, or threesteps. (b) Distribution of the three types of transition forces at 1.3 pN�s. Totally,102 observations were split into unkiss alone (�), double transition (E), and tripletransition (■ ). (c) Percentage of the three types of unfolding trajectories: three-step unfolding with an unkiss transition (light gray), two-step unfolding with adouble transition (black), and one-step unfolding with a triple transition (darkgray). Each column summarizes the results of at least 100 trajectories.

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a kinetic mechanism (Fig. 3a) with two premises: The unkiss isalways the first unfolding step, and the unkiss occurs over a largerange of the force. Therefore, the occurrence of the three types ofunfolding trajectories is determined by the unkiss. Because thekissing interaction broke at forces �16 pN, both hairpins remainedintact, and the unfolding appears to take three steps. When theRNA unkissed at forces �16 pN, hairpin 2 became unstable andquickly unfolded; the first unfolding step appears as a double-transition. If the kissing interaction survived until force was raisedabove F1/2 of hairpin 1, an apparent triple transition, in which twohairpins unfold right after the unkiss, occurred. Force distributionof the first unfolding transition categorized by the three types (Fig.3b) is consistent with this kinetic scheme.

When pulled faster, RNA structures tend to break at higherforces (2, 22). At higher loading rates, KC30 RNA unkisses athigher forces such that three-step unfolding becomes rare and thatoccurrence of the triple transition is more likely. This trend is clearlyshown in Fig. 3c. At 0.7 pN�s, �70% of the trajectories arethree-step. However, the occurrence of this type drops quickly asthe loading rate increases. At loading rates of 1.3 pN�s or higher,most trajectories show a single triple transition. The two-step curvesalways represent a small fraction of total trajectories, first increasingto �20% at 1.3 pN�s, then decreasing as the loading rate increases.

Therefore, force distribution of the first unfolding transitioneffectively reflects the kinetics of the unkiss. To extract kineticparameters of the unkiss, all of the first rip forces at 1.3 pN�s werepooled and analyzed by using the following equation (22):

ln{r ln�1�NF , r�} � ln[A�Xf3u‡ �kBT] � Xf3u

‡ �kBTF ,

[1]

where N(F, r) is the fraction of folded molecule at force F andloading rate r; A is the apparent rate constant at zero force (2, 21);Xf3u

‡ is the distance from the initial structure to the transition state;kB is the Boltzmann constant; and T is the temperature. Weobtained Xunkiss

‡ of 0.78 � 0.04 nm for breaking the kissing inter-action. Analyses of the force distributions collected at differentloading rates yield similar results (data not shown). From theforce-ramp experiments of the individual hairpins, we also obtainedthat the X‡ for disrupting hairpins 1 and 2 are 6.3 � 0.3 nm and 4.2 �0.2 nm, respectively (Table 1, which is published as supportinginformation on the PNAS web site). Noticeably, Xunkiss

‡ for breakingthe kissing interaction is significantly smaller than that for unfoldinghairpins. The difference in Xunkiss

‡ also is reflected in the rip forcedistribution because the value of X‡ is inversely correlated to thewidth of the rip’s force distribution. Most rips of hairpins 1 and 2occurred within a force range of 3 pN. In contrast, the unkiss forceranges from 7 to 30 pN at 1.3 pN�s (Fig. 3b).

The value of X‡ also reflects how the rate constant changes withforce. Eq. 1 was derived with the assumption that the dependenceof the rate constant, k(F), on force can be described by anArrehnius-like equation (23):

kF � k0eFX‡�kBT. [2]

For hairpins 1 and 2 with Xf3u‡ of �4–6 nm, the unfolding rate

constants rapidly increase with the force. From a narrow forcerange of �1–2 pN, such structural transitions occur either too fastor too slow to be detected. However, the small Xunkiss

‡ indicates thatthe rate constant of the unkiss transition can be measured over awide range of force.

Unkiss and Kissing Kinetics Measured by Force JumpTo verify this unusual force dependence of the unfolding kinetics,we measured the unkissing rate constants at forces ranging from13.5 to 30 pN by using a force-jump method (24). The applied forcewas rapidly stepped to a new value and the structural transitionswere monitored through changes in the molecular extension. The

rate constants of these transitions can be obtained from thelifetimes of the unreacted species. In a typical experiment (Fig. 4),force was quickly raised from 3 pN to a set force and held constant.The extension of the molecule remained constant until the unfold-ing occurred. For instance, the extension increased �30 nm upona triple transition at �20 pN. After being raised to 30 pN or higher,the force was kept constant for a few seconds to ensure that theRNA became single-stranded, before it was ramped down to�13–14 pN. The refolding of the two hairpins during the ramp wasindicated by the small zips in the extension. The force was thendropped to �7–8 pN to allow the kissing interaction between thehairpin loops, which was indicated by a decrease of the extension of�7–8 nm. After the kissing complex formed, the force was rampeddown to 3 pN before starting another cycle of experiments.

By using this approach, we followed the unfolding of KC30 RNAat various forces. As set force increased, the first unfolding transi-tion changed from the unkiss alone to a double transition, and thento a triple transition (Fig. 5). At forces ranging from 13.5 to 15 pN,�X of the first transition was �10 nm, consistent with the unkissalone. The two hairpins were intact until the force was further raised(data not shown). When the force was held constant between 15.5and 17 pN, �X of the first unfolding transition was �13–20 nm,suggesting that hairpin 2 unfolded along with the unkiss. When theforce was subsequently ramped up, hairpin 1 was unfolded atbetween 17 and 20 pN. The triple transition with �X of �30 nm wasobserved at forces of �17 pN. By using the worm-like-chaininterpolation formula (20), we calculated �X for the three types ofthe unfolding transitions (Fig. 5d). The measured values of �X foreach type of transition match the predicted values.

The force regions at which the three types of unfolding occurredare consistent with the force-dependent kinetics of disruptingindividual structures (Fig. 5d). The double transition occurred inthe same force region that hairpin 2 unfolds, but hairpin 1 remainsstable. The unkiss alone takes place below this force range, whereasthe triple transition occurred at forces no less than the unfoldingforce of hairpin 1. The rate-limiting effect of the unkiss step in theunfolding is most evident in the unfolding traces at �16 pN and at17.7 pN. At �16 pN, only after the double transition, the extensionof the molecule hops back and forth with a �X of �6 nm, indicatingthe hopping of hairpin 2 (Fig. 5b). At 17.7 pN, hairpin 1 hops oncethe triple transition occurred (Fig. 5c). The hopping rates of the

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Fig. 4. Unkiss and kissing transitions monitored at constant forces. (Upper)In a typical force-jump experiment, force was first quickly stepped from 3 to22 pN. (Lower) When a triple transition occurred, extension of the moleculeincreased by �30 nm. The force was then raised to 30 pN before being rampedto 14 pN. Next, the force was dropped rapidly to 8 pN. (Inset) The kissingshortens the extension by �7–8 nm. The detect position reflects the change inthe molecular extension.

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hairpins at these forces were visibly fast, whereas the both thedouble and triple transition, rate-limited by the unkiss, took secondsto occur.

Over 100 observations of the lifetimes of the kissing complex ateach force were pooled to generate the probability that the RNAhad not yet unfolded at a given time. This probability decays as asingle exponential function of time, indicating first-order kineticsfor the unkiss. The average lifetime of the kissing complex rangesfrom 1.6 s at 30 pN to 23 s at 13.5 pN (Fig. 6). By fitting the datato Eq. 2, we obtained Xunkiss

‡ of 0.65 � 0.8 nm, very similar to thevalue derived from the force-ramp experiments.

Because the kissing occurred at �7–8 pN, the hairpins could notform the kissing interaction again once the kissing is disrupted athigher force. Under such conditions, the hopping of each of the twohairpins can be monitored at their transition forces. The unfoldingand refolding rates of the hairpins near their F1/2 values are the sameas those of the individual hairpins within experimental error.Disruption of tertiary interactions is often irreversible (3). It istherefore possible to use the force-jump method to selectively breakcertain interactions and measure the rate constant of a specific step.In a recent study, a similar approach was used in atomic forcemicroscopy to study the steps in unfolding a protein (25). Asdemonstrated here, implementation of the force-jump method onthe optical tweezers also makes it feasible to dissect complicatedkinetics of folding a multidomain RNA.

This technique can also be used to measure the rate constant ofthe kissing, which occurred only after the formation of the hairpins(Fig. 4). We measured the kissing interaction at forces between 7.5

and 8.5 pN. At each force, the folding appears to follow first-orderkinetics. The rate constant of the kissing increases as the forcedeclines, as expected. We obtained a Xkiss

‡ of 4 � 1 nm by using Eq.2. For a simple hairpin that folds reversibly without stable inter-mediate, X‡ indicates the position of a single transition state alongthe reaction coordinate; the sum of Xf3u

‡ and Xu3f‡ should equal �X,

the change in the extension upon unfolding (21). However, the sumof Xunkiss

‡ and Xkiss‡ is only �5 nm, well short of the �X of kissing

(�7–8 nm). This observation suggests that the kissing and unkisstransitions involve multiple steps and that the transition states forthe forward and reverse reaction are different.

The folding free energy for the kissing interaction can beestimated from the force dependence of the unkiss and kissing rateconstants (Fig. 6). The rates become equal at �0.02 s�1 whenextrapolated to 9.9 � 0.2 pN. Both the worm-like-chain model (20)and experimental data give �X of 8.6 nm when the kissing complexis unfolded into two hairpins at this force (Fig. 5d). Hence,�G10.2 pN 22°C, which equals the reversible mechanical work tounfold the kissing interaction at this F1/2, is 85 � 2 pN�nm. Aftercorrection for stretching the single-stranded linker to F1/2 (2, 21),�G0pN 22°C 250 mM KCl, the kissing free energy at zero force, is 48 � 2pN�nm or 29 � 1 kJ�mol�1, comparable with a �G0pN 37°C 100 mM NaClof 27 kJ�mol�1 for the homodimeric minimal kissing complexmeasured by thermal melting (11). We also estimated the foldingenergy of hairpins 1 and 2 at zero force and 22°C as 69 � 11 and41 � 10 kJ�mol�1, respectively (Table 1).

DiscussionBecause the unkiss rate constant increases slowly with force atforces of �20 pN, under our experimental setup the unkissing rate

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Fig. 5. Step size of the first unfolding transition. (a–c) When KC30 RNA was unfolded at constant forces, the first transitions were unkiss alone, double transition,or triple transition. (b) At �16 pN, after the double transition, extension of the molecule hopped frequently, indicating the reversible unfolding of hairpin 2.(c) Similarly, hairpin 1 hopped at 17.7 pN once the triple transition occurred. (d) �X of the first unfolding transition as a function of force. Each value representsat least 100 observations. Œ, F, and ■ represent unkiss alone, double transition, or triple transition, respectively. Dashed curves are �X calculated by using theworm-like-chain interpolation formula (20). In these calculations, the persistence and contour length of a single strand are 1 nm and 0.59 nm per nucleotide,respectively; and the contour length of each base pair in the hairpin was assumed to be 0.3 nm.

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is significantly slower than the unfolding rate of the hairpins. Underthese forces, the unfolding rates of the two hairpins in the intactkissing complex are solely dependent on the rate-limiting unkissstep (Fig. 7a); the effective kinetic barrier for unfolding the hairpinscorresponds to the unkiss. Clearly, the kissing interaction signifi-cantly increases the kinetic stability of the two hairpins at highforces.

Such enhancement of the kinetic stability also is reflected by thehysteresis between the unfolding and refolding force–extensioncurves (Figs. 2 b and c and 7b). Particularly in the triple-transitioncurves, as force increased the hairpins were unfolded along with thekissing interaction at much higher forces than their normal unfold-ing forces. The unfolding forces of the hairpins is determined by theunkiss force. The hairpins do not experience the unzipping forceuntil the kissing interaction is disrupted. The hysteresis between theunfolding and refolding of the hairpins represents the extra me-chanical work required to unfold them in the presence of the kissinginteraction (Fig. 7b). This phenomenon is more pronounced athigher loading rates, under which single-step trajectories are dom-inant and unkiss forces are higher.

Our results provide an example that tertiary interaction enhancesthe kinetic stability of an RNA by blocking the transmission of forceto interior domains. The unfolding and refolding force–extensioncurves of L-21 ribozyme also display a large hysteresis (3). In thatcase, the rips were mapped to single-step unfolding of individualdomains consisting of both secondary and tertiary structures. Somerips occurred as high as 25 pN and were possibly rate-limited bydisrupting tertiary contacts. The refolding transitions, consisting ofa series of small transitions, were not assigned. We now think thata large plateau at �10–15 pN on the force–extension curve likelyrepresents sequential folding of secondary structures and that somezip-like transitions at lower force indicate formation of tertiaryinteractions. The hierarchy in RNA folding (1) demonstrated in thiswork probably also applies to the mechanical unfolding�folding ofL-21 ribozyme and other RNAs.

In the simplest scenario, disruption of the kissing interactionmust involve two steps (Fig. 8, which is published as supporting

information on the PNAS web site). First, the two kissing G�C pairsbreak, and then the two hairpins are pulled apart and the linker isstretched to an extension at which the tension matches the appliedforce, yielding most of the observable �X. The first step is presum-ably rate-limiting; consistently, Xunkiss

‡ is significantly smaller than�X, indicating that the position of the transition state is close to thekissing complex. The conformational change of the RNA at thetransition state is projected on the end-to-end extension as Xunkiss

‡ .The value of Xunkiss

‡ of �0.7 nm is roughly equivalent to the lengthof 2 bp. This value suggests two features of the unkiss: First, undertension, the helix axis of two kissing base pairs is nearly parallel tothe direction of applied force; second, both kissing base pairs arebroken at the transition state. The end-to-end distance of themolecule is therefore extended by 2 bp (Fig. 9, which is publishedas supporting information on the PNAS web site). Consistent withthese suggestions, the kissing base pairs and the two stems arestacked coaxially in the NMR structure and the phosphate-to-phosphate distance of the two kissing base pairs is �0.7 nm (11)(Fig. 10, which is published as supporting information on the PNASweb site).

The small value of Xunkiss‡ , 0.7 nm, means that the unkiss rate

constant is very insensitive to force, as compared with the rateconstants of the hairpins. The minimal kissing interaction showsslow unfolding rates of �0.05–0.5 s�1 over a broad force range from13 to 30 pN (Fig. 6). In contrast, unfolding and refolding rates of thehairpins change rapidly with the force. As a result, the two kissingbase pairs can survive a few seconds at 30 pN, whereas the lifetimesfor the hairpins are on the order of microseconds at this force. Suchan unusual mechanical stability of this minimal kissing complexagain indicates that both kissing base pairs are broken simulta-neously. Force, as a vector, affects molecular structure dependingon its direction. Hence, the geometry of the molecule relative to thedirection of applied force affects the mechanical stability. Forinstance, when a single piece of double-stranded �-DNA wasstretched from opposite ends, a overstretching transition occurredat �65 pN (19); however, when the �-DNA was unzipped from the5� and 3� termini at the same end, dissociation of the helix occurredat �15 pN (26). Unfolding of a hairpin is similar to unzipping the�-DNA because in both cases the direction of force is perpendicularto the structure and causes the ripping fork to proceed by breakingbase pairs sequentially (Fig. 11, which is published as supportinginformation on the PNAS web site). According to our hypothesis of

X ákiss = 4.1+0.7 nm

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Fig. 6. Rate constant in unfolding�refolding KC30 RNA. First-order rateconstants of unkiss and kissing were obtained from at least 100 observationsof lifetimes. Œ, F, and ■ represent unkiss alone, double transition, or tripletransition, respectively. } indicates the kissing. Dashed lines are fits to Eq. 2.Unfolding and refolding rates of hairpins 1 and 2 (Table 1) were estimatedfrom the results of force-ramp experiments (2, 22). For hairpin 1, lnkf3u (1.46 � 0.07)F � (23.9 � 0.3) and lnku3f (�1.36 � 0.06)F � (25.4 � 0.3). Forhairpin 2, lnkf3u (1.02 � 0.05)F � (15.3 � 0.3) and lnku3f (�1.35 � 0.06)F� (24.4 � 0.3). Hopping rates at F1/2 for both hairpins are consistent with theseextrapolations (data not shown).

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a bEnergy landscape to unfold the kissing complexat high force

Fig. 7. Rate-limiting effect of the unkiss. (a) At high forces, the effective kineticbarrier for the overall unfolding is the one to break the kissing. (b) When a tripletransition occurs at high force (blue), the first part of the rip is to unkiss; the restis the unfolding of the hairpins. The area under the rip for unfolding the hairpins(green)equals themechanicalworkdonetounfoldthetwohairpins inthekissingcomplex, which is significantly larger than the mechanical work to fold thehairpins (orange areas). This difference and the hysteresis between the unfoldingandrefoldingcurves reflect theenhancedkinetic stabilityof thehairpins imposedby the rate-limiting kissing interaction.

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kissing loops described above, the force is parallel to the axis of thekissing base pairs, similar to the geometry in stretching the �-DNAfrom the opposite ends. Under such shearing force, multiple basepairs need to break simultaneously to cause a structural transition;therefore, more resistance to the mechanical perturbation isexpected.

We have observed that the sum of Xunkiss‡ and Xkiss

‡ is smallerthan �X. These observations suggest that the transition state ofthe kissing is different from that of the unkiss. The kissing rateconstant is determined both by the strength of the interactionand by the distance between the two loops. The latter iscontrolled by the tension and the length of the single-strandedlinker. We notice that the apparent Xkiss

‡ is roughly half of �X(Fig. 6), indicating that intramolecular diffusion plays an impor-tant role in determining the kissing rate.

In summary, we have found that this minimal kissing complex hascharacteristics distinct from those of secondary structures: the twokissing base pairs broken simultaneously by force, small Xunkiss

‡ anda nearly force-independent unfolding rate constant, relatively highmechanical stability, and increased folding irreversibility as indi-cated by the hysteresis between forward and reverse reactions. Thehierarchy of RNA force folding is evident. Breaking the tertiarycontact is the first unfolding step and becomes rate-limiting at highforce; the kissing interaction forms last, only after the hairpins havefolded. Further investigations are required to test whether thesefeatures are general to RNA tertiary structures.

Is the mechanical property of this RNA kissing complex impor-tant to the dimerization of retroviral RNAs? One clue comes fromevolution. The kissing hairpins are found in all characterizedretroviral DIS region. For instance, DIS of Moloney murinesarcoma virus contains two kissing hairpins with GACG loops (27).As we demonstrate here, even a minimal kissing complex with twoG�C pairs is mechanically stable at 22°C, consistent with previousresults from thermal melting and NMR studies (11). The presenceof multiple kissing complexes surely increases the stability of RNAdimers and can speed the dimerization (18).

However, several ‘‘kissable’’ hairpins with the same loop cancause mismatch problems. In MMLV, the DIS�� region containsfour kissable hairpins, two of each kind (Fig. 12, which is publishedas supporting information on the PNAS web site). In the maturevirus, the viral RNA dimer eventually evolves into a mature form,in which the first two kissing complexes (formed by SL-A and SL-B)are converted into extended duplexes and the other two kissingcomplexes may or may not exist in the final dimer (9, 10). However,mismatched kissing interactions, such as the one with SL-C fromone RNA kissing SL-D from another strand, can also be formed.The mismatched kissing interactions in such dimers have to bedisrupted before the mature dimer can be formed. We hypothesizethat the relatively force-insensitive unkiss rate provides the minimal

kissing complex almost constant stability over a large range of force;yet, even at low force, this structure is breakable in minutes,allowing it to form the correct kissing pairs or be rearranged intoa mature duplex structure. The mechanism by which viruses solvethis mismatch problem is a question for future research.

Materials and MethodsPreparation of RNA. All four RNAs were cloned into pBR322vector between the EcoRI and HindIII sites. Both KC30 andKC30AA RNA contain a 30-nt linker between the two hairpins.The linker sequence is 5�-AAAAA UAUCG AAAAA AATACCAAAA AAAAA-3�. Hairpin 2 in KC30AA RNA contains anapical loop of GAAA. The plasmids were used as a template forPCR to produce a �1.2-kb DNA containing the inserted se-quence and two flanking ‘‘handles’’ �500 bp long. This DNAalso had a T7 promoter to be used as a template for in vitrotranscription of the RNA with handles. DNA molecules withsequence complementary to the handles were also generated byPCR. Then the RNA and two DNA handles were annealed. TheDNA handle upstream of the kissing structure was biotinylatedat the 3� end, and the downstream DNA handle contained adigoxigenin group at the 5� terminus. Through affinity interac-tions, the annealed molecule can be attached to a pair of beadscoated with streptavidin and antidigoxigenin antibody, respec-tively (Fig. 1).

Optical Tweezers. Dual-beam optical tweezers (28) were used tostudy the folding of the kissing RNA. In a flow chamber, thestreptavidin-coated bead was held by a force-measuring opticaltrap. The antidigoxigenin-coated bead was mounted on the tip ofa micropipette by suction. The position of the micropipette wascontrolled by a piezoelectric flexure stage. By moving the micropi-pette, the extension of the molecule was changed, which inducedtension on the molecule. Change in the extension of the moleculewas measured by the relative movement of the trapped bead and thepiezoelectric flexure stage.

Folding Experiments. All unfolding�refolding experiments weredone at 22°C in 10 mM Hepes, pH 8.0�250 mM KCl�1 mMEDTA�0.05% NaN3. In the force-ramp experiments, the piezo-electric flexure stage was moved in one dimension at a constant rate(nm�s), which generated a roughly constant loading rate (pN�s)between 3–30 pN. The force-jump experiments used a feedbackcontrol to maintain constant force (24). Force and extension of themolecule were recorded at a rate of 100 Hz.

We thank Ms. Maria Manosas, Mr. Jeff Vieregg, Dr. Gang Chen, and Dr.Felix Ritort for critically reading the manuscript. This work is supportedby National Institutes of Health Grants GM-10840 (to I.T.) and GM-32543 (to C.B.).

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15852 � www.pnas.org�cgi�doi�10.1073�pnas.0607202103 Li et al.

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